Question: Solve for $x$ and $y$ using elimination. ${x-2y = -3}$ ${-x-3y = -27}$
Solution: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the top and bottom equations together. $-5y = -30$ $\dfrac{-5y}{{-5}} = \dfrac{-30}{{-5}}$ ${y = 6}$ Now that you know ${y = 6}$ , plug it back into $\thinspace {x-2y = -3}\thinspace$ to find $x$ ${x - 2}{(6)}{= -3}$ $x-12 = -3$ $x-12{+12} = -3{+12}$ ${x = 9}$ You can also plug ${y = 6}$ into $\thinspace {-x-3y = -27}\thinspace$ and get the same answer for $x$ : ${-x - 3}{(6)}{= -27}$ ${x = 9}$